Links and Resources

This RISP activity introduces the subject of differentiation. Rather than start from first principles or learning a rule, the activity suggests using a graphing package to generate data. Starting with a quadratic graph, students find the gradient of the curve using a straight line graph and are encouraged arrive at a rule for differentiating a power of x through pattern spotting.

The RISP resource, Differentiation 2, contains four further investigations to explore differentiation.

Additionally, the 'Mostly Algebra' collection contains the resource A14 Exploring Equations in Parametric Form, in which students find and determine the nature of stationary points when a function is given in parametric form and find the intercepts of the function.

These fourteen resources from Mathcentre cover a range of topics including the chain rule, product rule and quotient rule, differentiating a range of functions and differentiation from first principles. Each resource contains detailed notes, examples and questions to be completed, with answers.

This Active A level resource from Susan Wall contains eleven problems that require students to explore where turning points occur, match statements about functions, derivative functions and gradients, explore the tangent and normal to a curve, suggest a possible graph given information about the function, the gradient of the function and the rate of change of the gradient of the function.

In addition the Further Indices resource contains a large matching activity involving equivalent functions, differentials and integrals with a range of different indices.

This interactive excel file from The Virtual Textbook plots both quadratic and cubic functions along with the graphs of their first and second differential equations. By specifying the values of the functions students can see the effect this has on the graphs of the function, first differential and the second differential. The resource also include a number of student worksheets.

The first of these three videos from Casio explores the function y = x/(16+x2), finding the stationary points by rewriting the equation and using the product rule. The video also shows how to find the value of the differential of y= (1+e3x)5/3 using the chain rule.

The two further videos explore graphical solutions when finding stationary points by using a calculator to draw the graph and find the coordinates of the maximum and minimum values, and how to use a graphic calculator to verify solutions.

These two instructional videos from Casio explain how to use a graphical calculator to find the value of the first and second derivatives of a given function at specific values for x, and how to find the derivatives at specific values of x in order to verify the solution.